# Fine-grained Generalization Analysis of Structured Output Prediction

arXiv: https://arxiv.org/abs/2106.00115 · HTML: https://mlsanity.com/paper/2106.00115/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 31 May 2021.

## Builds on (most cited first, 14 of 14)

- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Show and Tell: A Neural Image Caption Generator](https://mlsanity.com/paper/1411.4555/) (2014)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Norm-Based Capacity Control in Neural Networks](https://mlsanity.com/paper/1503.00036/) (2015)
- [A vector-contraction inequality for Rademacher complexities](https://mlsanity.com/paper/1605.00251/) (2016)
- [Fine-Grained Analysis of Stability and Generalization for Stochastic Gradient Descent](https://mlsanity.com/paper/2006.08157/) (2020)
- [A Consistent Regularization Approach for Structured Prediction](https://mlsanity.com/paper/1605.07588/) (2016)
- [Structured Prediction Theory Based on Factor Graph Complexity](https://mlsanity.com/paper/1605.06443/) (2016)
- [Rademacher Complexity Bounds for a Penalized Multiclass Semi-Supervised Algorithm](https://mlsanity.com/paper/1607.00567/) (2016)
- [Multi-class SVMs: From Tighter Data-Dependent Generalization Bounds to Novel Algorithms](https://mlsanity.com/paper/1506.04359/) (2015)
- [Localized Structured Prediction](https://mlsanity.com/paper/1806.02402/) (2018)
- [Fine-grained Generalization Analysis of Vector-valued Learning](https://mlsanity.com/paper/2104.14173/) (2021)
- [Rademacher Complexity and Generalization Performance of Multi-category Margin Classifiers](https://mlsanity.com/paper/1812.00584/) (2018)

## Built on by (most cited first, 4 of 4)

- [Generalization Analysis for Supervised Contrastive Representation Learning under Non-IID Settings](https://mlsanity.com/paper/2505.04937/) (2025)
- [Conv4Rec: A 1-by-1 Convolutional AutoEncoder for User Profiling through Joint Analysis of Implicit and Explicit Feedbacks](https://mlsanity.com/paper/2509.07499/) (2025)
- [Generalization Analysis on Learning with a Concurrent Verifier](https://mlsanity.com/paper/2210.05331/) (2022)
- [Explainable Neural Networks with Guarantees: A Sparse Estimation Approach](https://mlsanity.com/paper/2501.02010/) (2025)

## Abstract (arXiv)

In machine learning we often encounter structured output prediction problems (SOPPs), i.e. problems where the output space admits a rich internal structure. Application domains where SOPPs naturally occur include natural language processing, speech recognition, and computer vision. Typical SOPPs have an extremely large label set, which grows exponentially as a function of the size of the output. Existing generalization analysis implies generalization bounds with at least a square-root dependency on the cardinality d of the label set, which can be vacuous in practice. In this paper, we significantly improve the state of the art by developing novel high-probability bounds with a logarithmic dependency on d. Moreover, we leverage the lens of algorithmic stability to develop generalization bounds in expectation without any dependency on d. Our results therefore build a solid theoretical foundation for learning in large-scale SOPPs. Furthermore, we extend our results to learning with weakly dependent data.